Would water have a higher or lower boiling point if it were linear instead of bent?

Water as a bent molecule:

Water molecules have a bent molecular shape. This occurs because of the presence of unshared electrons on the oxygen atom.

The presence of unshared electrons on the oxygen atom results in a molecule with unequal charge. The oxygen side of a water molecule has a partially negative charge, while the hydrogen side has a partially positive charge. When molecules have unequal charge, they are called polar molecules.

Polar water molecules are held together by medium strength intermolecular forces called hydrogen bonds. 

Water as a linear molecule:

If order for water to have a linear molecular shape, the unshared electrons on the oxygen atom would have to be absent.

Without the unshared electrons on the oxygen atom, the water molecule would not have partial negative and partial positive charge. The charge on a water molecule would be evenly distributed across the molecule. Molecules with evenly distributed charge are called nonpolar molecules.

Nonpolar molecules are held together by very weak intermolecular forces called dispersion forces. 

Comparison of boiling points:

Since the intermolecular forces that hold together polar molecules are stronger than the intermolecular forces that hold together nonpolar molecules, more heat energy will be needed to disrupt the intermolecular forces holding the molecules together. This would result in a higher boiling point for polar molecules. 

Therefore, if water was linear, it would have a lower boiling point because the intermolecular forces holding the water molecules together would be weaker.